Bayesian Rationality and Social Epistemology
Social life comes from a double source, the likeness of consciences
and the division of social labor.
There is no such thing as society. There are individual men and
women, and there are families.
At least since Schelling (1960) and Lewis (1969), game theorists have interpreted social norms as Nash equilibria. More recent contributions based upon the idea of social norms as selecting among Nash equilibria include Sugden (1986), Eister (19891,b), Binmore (2005), and Bicchieri (2006). There are two problems with this approach. The first is that the conditions under which rational individuals play a Nash equilibrium are extremely demanding (theorem §8.4), and are not guaranteed to hold simply because there is a social norm specifying a particular Nash equilibrium. Second, the most important and obvious social norms do not specify Nash equilibria at all, but rather are devices that implement correlated equilibria (§2.11, §7.5).
Informally, a correlated equilibrium of an epistemic game G is a Nash equilibrium of a game G+, in which G is augmented by an initial move by a new player, whom we call the choreographer, who observes a random variable γ on a probability space (Γ, p), and issues a “directive” fi(γ) ɛ Si to each player i as to which pure strategy to choose. Following the choreographer's directive is a best response for each player, if other players also follow the choreographer's directives.
This chapter uses epistemic game theory to expand on the notion of social norms as choreographer of a correlated equilibrium, and to elucidate the socio-psychological prerequisites for the notion that social norms implement correlated equilibria.
The correlated equilibrium is a much more natural equilibrium criterion than the Nash equilibrium, because of a famous theorem of Aumann (1987), who showed that Bayesian rational agents in an epistemic game G with a common subjective prior play a correlated equilibrium of G (§2.11–2.13).